a trading strategy based on Elliott Wave Theory - page 261
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Интересный был бы вариант и с термодинамической системой, но емкости и индуктивности - чтой-то не очень. ИМХО.
Agreed.
The differential equations describing the oscillations of a system in the presence of dissipation forces are the same in mechanics and in electrical engineering, hence the systems of equations for these processes are similar. Therefore, it makes no sense to talk about which analogy is better. It is more important to identify the laws to which the phenomenon under study obeys, and to describe these laws by a system of difurcations is a matter of technique and time.
If the matter were limited to "oscillations of the system in the presence of dissipation forces", it would be so. There is, however, one great subtlety here. When mechanical stresses occur in the medium that exceed the limits of its elasticity, it turns into a viscous fluid. These are quite different, moreover, non-linear diffusions. Nevertheless, the system continues to exist and processes develop there with limited speed.
And what corresponds to this in electrical circuits? A capacitor breakdown? Short circuit?
In tensile testing of metal specimens, mechanical stress is determined when the yield phase reaches its limit and the specimen bursts. In my opinion this would correspond to a breakdown or short circuit. But which state of an electrical circuit corresponds to the state of a viscous (or rather very viscous) fluid in continuum theory ? How many of you know?
By the way, for that matter, market fluctuations can hardly be called dissipative in the full sense of the word. In the presence of dissipative forces, oscillations are notoriously damped. And in the market fluctuations never damp down to zero. On the contrary, the market is characterized by a certain level of swing around which all events occur. Even if the oscillations decrease when all three sessions are over, it's temporary and the amplitude is restored during any of the sessions. To me it looks more like quantum mechanics: zero fluctuations at absolute zero temperature. And the transition to a new price level often happens as a tunnel transition, if the resistance (or support) is too strong for the market to break through it in the process of movement. In this case, price overcomes this level by leaps and bounds, and this does not necessarily happen on the news.
IMHO. If you try to reduce everything to a system of diff equations describing the system, it will no longer be an analogy. It would already be a complete transposition of the model. And hardly anyone would dare to say that any of known physical models (classical or quantum) is adequate to the mess going on in the market. :-))
I am not ready to prove that any field of physics contains analogues of all the phenomena from other fields. First of all because I don't think so.
IMHO:
Temperature is naturally associated with the market (degree of crowd). That is, it is higher during the sessions and the swing is also higher. It seems obvious and the presence of positive feedback - movement provokes panic, panic intensifies movement, intensification of movement intensifies panic, etc. (quite similarly, power released when current flows warms up a resistor, if it is, for example, a semiconductor - its resistance decreases, this leads to an increase in current, i.e. further warming, etc.). From quantum mechanics the notion of density of states comes to mind. I don't know about tunneling, someone may call it passing a bifurcation point, but sometimes a strong kick is apparently enough :), and even not too strong in a thin or heated market. And between kicks (catastrophes, transitions) it is quite similar to dissipative behaviour.
That's what I don't get. Are all models the same? Simply, the better a prototype is chosen, the fewer additions and changes will be needed. The criterion is not our tastes and preferences, but the laws to which the studied phenomenon submits ((c) Neutron:).
Exactly ! If we take the whole system of diphires, which describes the phenomenon, it means that we completely accept the corresponding model for the market and therefore we transfer the laws acting for the model to the market. If we limit ourselves to analogy, it is obviously some approximation and nothing more.
For example, Vladislav in his model accepted the analogy of market fluctuations with the fluctuations of a mechanical system in a potential pit. Thus potential energy he approximated by a quadratic form. And that's all! He did not try to find an exact analytical expression of potential energy, did not solve Newton's equations, did not build a price trajectory, i.e. did not do everything for the sake of which the diffusions are written.
Also in principle it is not a crime, if we treat it as the first approximation. However, again, it depends on what to call an analogy.
In this formulation, the relaxation character of the sought value with time is of interest, and two cases are distinguished:
1. the price has infinite rigidity with respect to its moving average (Wiener process);
2. the price has finite rigidity, i.e. not only the moving average (MA) runs after the price, but the price tends to it;
Suppose that the interaction force of price and MA is described, in general terms, by a power polynomial, then we have to construct a system of equations relating the rigidity factor, distance between price and MA and relaxation nature with coefficients of the power series.
It seems to be possible to solve this problem in the general form and thus the output will contain the direction and value of the force acting at that moment on the price series. It is more than enough for forecasting.
One more thought.
Let's look at swaps on short CFD positions:
#AA ALCOA INC 100 shares 10% 0.03 0 .10 -8.28% 2.66%
#AIG AMER INTL GROUP 100 shares 10% 0.04 0 .10 -8.28% 2.66%
#AXP AMERICAN EXPRESS CO 100 shares 10% 0.03 0 .10 -8.28% 2.66%
...
...
#WMT WAL-MART STORES INC 100 shares 10% 0.04 0 .10 -8.28% 2.66%
#XOM EXXON MOBIL CORP 100 shares 10% 0.03 0 .10 -8.28% 2.66%
We see that 2.66% of short position swap equals 3%-10% Spread (0.03-0.1).
Suppose that the average daily volatility of the instruments is about n points. Let us have a portfolio of N instruments. Assume that in the first approximation price behavior is random. Then having opened short positions for all instruments we have a synthesized instrument with daily volatility sigma0=n/SQRT(N). In the worst case, this instrument will be negative against us by the value: V=sigma0*SQRT(T/T0), where T- time of holding positions open in days, T0 - 1 day. On the other hand, every day we will receive a return on swaps: v=Swap*T/T0. v grows linearly, V is a square root, it is obvious that at some point v necessarily becomes larger than V, and we will be in the black!
sigma0*SQRT(T/T0)=Swap*T/T0 from where it follows: T=T0*(n/SQRT(N)/Swap)^2.
Assuming T0=1 day, n=100/day, N=100 symbols and Swap=2 points/day we get Т=10 days, i.e. even in the worst case when the whole combined position went against us, in about 10 days we will be in the plus and gain consistently 2 (more precisely 2.66) points a day. In a year, this is an iron 500 points with a deposit of 100 instruments of 0.1 lot and 1:10 leverage - it is $130*100*10= $100000 (approximately). This corresponds to 500*0.1*$10*N=$50000 per year with minimum risk or 50% per annum. If only 10 instruments are left in the portfolio, the deposit can be reduced to $10000 with a 3-fold increase in market risk.
This swap trading looks tempting, if only to find where to get $10000 :-))
The second seems more vital to me. But is that enough for at least a first approximation? I do not have coherent enough thoughts of my own yet, I will limit myself to quoting from Peters:
... we need an alternative statistical model that has distributions with thick tails, exhibits persistence and has unstable variance.
There is a class of noise processes that meets these criteria: 1/f or fractional noise ...
...
1/f-noise is closely related to relaxation processes. In fact, 1/f-noise was postulated by Mandelbrot (1982) as the sum of a large number of parallel relaxation processes occurring at many different frequencies.
Yes, it does look tempting. But I wouldn't look for $10000 until I found out the catch. :-))
And that there is one, I have no doubt.
http://betaexpert.narod.ru/trademath.htm (Prelude written in the author's traditional style ;o))
And here are some tricky calculations of short positions
http://forum.cgm.ru/lofi/f26/th8142.html
I have not figured it out myself. I am posting it in case it will be useful for someone, since we are talking about trading for swaps and similar tricks.
Yura, I'm far from such ideas.
Yesterday I ran about 30 CFD instruments on the demo. Here is what I get:
1. Average volatility of the instruments in the portfolio - 50 pips per day;
2. Average volatility of the portfolio - 10 pips per day. This corresponds well with the model: sigma0=n/SQRT(N)=50/SQRT(30)=9 points a day;
3. the average price of one point of a standard lot is $1;
4. the average margin for a standard lot is $700;
5. the average spread value is 4 points;
6. the average swap value of short positions is +0.4 points a day.
That's the story. Let's see what follows:
T=T0*(n/SQRT(N)/Swap)^2=1*(50/SQRT(30)/0.4)^2=500 days!!! and we're broke even :-(
Yeah, we cannot trade with swaps on CFD... At least not on these terms.
As far as I'm concerned, there is an interesting point to be made.
I do not know if anyone has noticed that although the price increment in CFD instruments as well as in currency pairs is a random value (to a first approximation), the absolute value of the price increment is directly proportional to the value of the asset! In other words, the swing of price series is proportional to the value of the asset. In currencies there is no such thing! Thus, if the portfolio contains a sufficient number of CFD instruments and we open long positions with all of them, at the initial moment in time we will be in the statistical zero (half growth in stocks, half growth in stocks) minus spread, minus commission and minus swap of long positions. The last two components can be safely ignored compared to the spread (see above). But after a certain amount of time, with a numerical equal of plus and minus price increases due to the difference in the absolute average value of the increments of rising stocks and falling stocks, we will come out in a solid plus!
I don't think logic suffers.
to Candid
... we need an alternative statistical model that has distributions with thick tails, exhibits persistence and has unstable variance.
There is a class of noise processes that meets these criteria: 1/f or fractional noise ...
...
1/f-noise is closely related to relaxation processes. In fact, 1/f-noise was postulated by Mandelbrot (1982) as the sum of a large number of parallel relaxation processes occurring at many different frequencies.
Candid, can I have a link to that print?
Besides, such models exist and perfectly simulate the behaviour of residuals in time series by distribution function (fat-tailed distributions) and by autocorrelation function (persistence). These are autoregressive models of infinite order. It is a great thing and it predicts the behavior of the simulated series very well but it has a limit in terms of the maximum yield - it barely covers the existing spreads. For example, if we keep the spread not larger than 1 point at EUR/GBP twenty-four hours a day, then the annual return of the AR-model will be 10 000 points! The same can be said about EUR/CHF (20000-30000 points a year). If spread at these pairs is 2 points, the annual return will fall to 200-400 points, if it is 3 points, we lose points. But for EUR/USD the border of profitability lies in the area of 0.5 points, i.e. unreal spread.